Verizon claims that AT&T has a similar amount of spectrum as Verizon does, and should work harder to design their networks to use that spectrum efficiently. Personally, I think AT&T was crying wolf to get the FCC to agree to the T-Mobile merger. They seem to be doing just fine in their initial markets without it. At some point they will transition the existing GSM/EDGE/3G network to use LTE because LTE can also handle voice along with data (right now most LTE phones only use LTE for data, it will take a few years). In fact, that would be the logical evolution for Verizon as well, but that's a bigger change for them since they use CDMA rather than GSM.

In some markets like Chicago, AT&T has a single wide band for LTE rather than the more desirable double wide band (to put it in accessible terms), so LTE isn't as fast there as it in in Dallas where they have plenty of spectrum width.